so realistically we should be seeing other “giant axes” if they were for processing mammoths.

We do! Here are some from egypt, 500,000 years ago: https://blogs.ucl.ac.uk/researchers-in-museums/tag/handaxe/

The great Furze Platt handaxe is 400,000 years old and from Britain: https://joyofmuseums.com/museums/united-kingdom-museums/london-museums/natural-history-museum-london/great-handaxe-from-furze-platt/

And here are 300,000 thousand years old ones from Spain: https://theconversation.com/giant-handaxes-suggest-that-different-groups-of-early-humans-coexisted-in-ancient-europe-91977

Edit: On that note, here’s a giant handaxe where I have no doubt believing that it could be a prestige object: The giant handaxe of West-Tofts with a carefully preserved shell!